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A significant number of servers that constitute the Internet are to provideprivate data via private communication channels to mutually anonymousregistered users. Such are the servers of banks, hospitals that provide cloudstorage and many others. Replacing communication channels by maximallyentangled states is a promising idea for the quantum-secured Internet (QI).While it is an important idea for large distances secure communication, for thecase of the mentioned class of servers pure entanglement based solution is notonly unnecessary but also opens a threat. A crack stimulating a node togenerate secure connections via entanglement swapping between two hackers cancause uncontrolled consumption of resources. Turning into positive a recentlyproven no-go result by S. B\"auml et al. [15], we propose a naturalcountermeasure against this threat. The solution bases on connections betweenhub-nodes and end-users realized with states that contain secure key but do notallow for swapping of this key.We then focus on the study of the quantum memorycost of such a scheme and prove a fundamental lower bound on its memoryoverhead. In particular, we show that to avoid the possibility of entanglementswapping, it is necessary to store at least twice as much memory than it is thecase in standard quantum-repeater-based network design. For schemes employingeither states with positive partial transposition that approximates certainprivates states or private states hardly distinguishable from their attackedversions, we derive much tighter lower bounds on required memory. Ourconsiderations yield upper bounds on a two-way repeater rate for states withpositive partial transposition (PPT), which approximates strictly irreducibleprivate states. As a byproduct, we provide a lower bound on the trace distancebetween PPT and private states, shown previously only for private bits.

Hybrid quantum network design against unauthorized secret-key generation, and its memory cost